Multiplicative noise removal combining a total variation regularizer and a nonconvex regularizer

Abstract

A novel variational model for removing multiplicative noise is proposed in this paper. In the model, a novel regularization term is elaborately designed which is inherently equivalent to a combination of the classical total variation regularizer and a nonconvex regularizer. The proposed regularization term, on the one hand, can better remove the noise in homogeneous regions of a noisy image and, on the other hand, can preserve edge details of the image during the denoising process. In order to solve the model efficiently, we design an alternating iteration process in which two coupling minimization problems are solved. For each of the two minimization problems, the existence and uniqueness of their solutions are proved under some necessary assumptions. Numerical results are reported to demonstrate the effectiveness of the proposed regularization term for multiplicative noise removal.

Keywords:

• denoising
• multiplicative noise
• total variation
• nonconvex regularizer
• alternating iteration

2010 AMS Subject Classifications:

• 68U10
• 65F22
• 65K10
• 65F10
• 65N55

Acknowledgements

The authors would like to acknowledge the support of The Hong Kong Research Institute of Textiles and Apparel for this work. Thanks to Esquel Enterprises Limited, Babei Group Company Limited and TAL Apparel Limited. This paper is supported by the NSFC 61105011, 61271294 and 11101292, the Hong Kong RGC GRF Grants PolyU 5101/11E and 5100/12E, the DFMEC 20134408110001 and the Hong Kong ITC/HKRITA Project ITP/002/10TP.